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1. the way to right an exponentional is a*b^x, where a=initial, b=rate, and x=x.the initial value here is 2. The rate is 3 because in order to get from 2 to 6, you multiply 3, and in order to get from 6 to 18, you multiply by 3.

so your equation is 2(3)^x.

2. So carter initially sends 10 posts, and they further send 2. So a=10 and b=2.

10(2)^x.

3. So you can use desmos.com and plot out the graph. See the attachment for the graphs. the blue=amber, green=ben, orange=carter.

4. Just just plug in x=3 and x=10 for all the functions.

Amber - when x is 3, it's 192. when x is 10, it's 3145728 (DANG THAT'S HUGE)

ben-when x is 3, it's 54. when x is 10, it's 118098

carter - when x is 3, its 80. when x is 10, it's 10240.

5. It shifts the graph 45 units upward. it is a rigid translation. so the y intercept is 48.

6. Amber because the rate is the highest. for a while, the others may be slightly ahead, but then amber's graph takes over and she gets the most posts.

7. If you'd want the post to spread like wildfire, you'd want to want to have a graph similar to Amber's, where the shares are more but less initial friends. This can be seen because the graph of Amber's has a much faster spread rate than the other graphs. Also, when comparing similar points, Amber always had the most shares.

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step-by-step explanation: